喷射造型中残余应力的数值模拟外文文献翻译、中英文翻译

Numerical Simulation of Residual Stress in Injection MoldingXI Guo-dong, ZHOU Hua-min, LI De-qun (State Key Laboratory of Mold &Die Technology, Huazhong University of Science and Technology, Wuhan 430074, China)Abstract: Distribution and history of residual stress in plaque-like geometry aresimulated based on linear thermoviscoelastic model, to explore the mechanics and evolution of residual stress in injection molding process. Results show that the residual stress distribution through thickness is almost the same along flow path and the stress value near the end is a litter higher than that near the gate.CLC number: TQ 320.66；O 345 Document code: A Article ID:1003-4951(2006)01-0017-07Keywords: injection molding; residual stress; numerical simulation; thermoviscoelastic1 IntroductionInjection molding is a flexible production technique for the manufacturing of polymer product. A typical injection molding process consists of four stages: filling, packing, cooling and ejection of product. During these processes, residual stress is produced due to high pressure and cooling, which induce the warpage and shrinkage of product. To make the product with high precision, it is important to simulate the pressure and thermal effect induced residual stress in the processes. Residual stress of injection molding has received more and more attention recently. Many researchers15 calculated the residual stress and shrinkage in the process by using different models.In general, the study of residual stress is focused on the theoretical analysis with an isolated model. It does not take into account the specifics of injection molding and correlate with the packing and cooling analysis. In this study, distribution and history of residual stress in plaque-like geometry is simulated based on linear thermoviscoelastic model, where the effects of pressure, thermal history and stress relaxation are jointly investigated.The numerical calculation model is built by finite difference method in time duration with layered discretization along thickness and under the specified boundary conditions. The developed simulation system is used to calculate the residual stress of typical injection molded parts.2 Model Problem2.1 Linear Thermoviscoelastic ModelTemperature and pressure induced stresses arise from inhomogeneous cooling of the part in combination with the hydrostatic pressure. For cooling, the relaxation time increases and becomes comparable to the filling and packing time; therefore accurate prediction of thermal stress would require viscoelastic constitutive equations.But within the limit of infinitesimal strains variation the behavior of viscoelastic material is well described by the theory of linear viscoelasticity. Most injection mould products are very thin, we can take the flow direction as 1-dimensional and the local thickness direction as the 3-direction and build the local coordinates. The total stress tensor ij can be split into a hydrostatic pressure h P and an extra stress part ij 6Where G1 is bulk relaxation function, G2 is shear relaxation function, th is thermal strain, mis spherical strain tensor,ij extra strain tensor and (t) is the material time.2.2 Basic Assumptions and Boundary ConditionsFor simplifying the calculation of thermally and pressure induced stress in the injection molding process, the following assumptions are made:(1) We take the flow direction as the 1-direction and the local thickness direction as the 3-direction and build the local coordinates; (2) While in the mold, the material is locally constrained in the in-plane directions by three dimensional features of the part (bosses, ribs and other walls), so the in-plane strain is assumed to be equal to 0; (3) The normal stress 33 is constant in the thickness direction of the product and equals the reverse of cavity pressure; (4) As long as the cavity pressure is non-zero ( 0 33 ), the material sticks to the mold walls; (5) Mold elasticity is neglected and the warpage of wokpiece in the mold is not taken into account.3 Results and DiscussionTo study the evolution and distribution of stress, simulation is performed for a fan-gated specimen (300752.5 mm) as shown in Fig.1. A minimum complexity approach is proposed to emphasize the process physics, which would result in a better understanding of the transition that takes place during the molding. The material used was ABS (Novodur P2X of Bayer). The material parameters and the main processing parameters are listed in Table 1 and Table 2, respectively.Fig.1 Rectangular strip mold3.1 Evolution of Cavity PressureAccording to the Basic Assumptions (3),normal stress equals the negative of the packing pressure in simulation. Therefore, the evolution of cavity pressure shows the variation of normal stress. Fig.2 shows the calculated pressure history at different locations along the flowpath, including the pressure profiles near the gate, quarter to the gate, halfway down to the end, quarter to the end and near the end of the flowpath. During filling, the pressure increases to overcome the increasing resistance to flow. At the end of the filling stage, the maximum pressure (63.42MPa) is near the gate and the minimum pressure (15.62MPa) is near the end of flow. There is an obvious difference between these two locations. When the packing stage begins, cavity pressure at all locations increases and is close to the setting packing pressure 60 MPa quickly. Moreover,the pressure distribution tends to be uniform. At the packing stage, material is forced into the cavity to compensate for the shrinkage that occurs during cooling. The cavity pressure mainly holds constant at first, then decays slowly as the frozen layer grows toward the core region. The location near the end is harder to compensate for shrinkage, where the cavity pressure drops more quickly. The cavity pressure tends to be nonuniform in the flowpath. At the end of packing, the pressure near the gate is 50.99MPa, while the pressure is just 36.75MPa near the end of flowpath. Then, cavity pressure all over Numerical Simulation of Residual Stress in Injection Molding the part drops at the same speed as the continuous cooling. After cavity pressure drops to zero, the part is detached from the mold in the thickness direction and shrinks freely. The normal stress keeps zero. Fig.2 Calculated pressure history for specimen at different locations along the flowpath3.2 Evolution of Residual StressWe call the stress in the flow plane “in-plane stress”. To the transversely isotropic material, x-direction stress equals y-direction stress. Fig.3 and Fig.4 show the in-plane stress distribution in the thickness direction and its evolution in the central position P1 plotted in Fig.1. Fig.3 shows the whole evolution of in-plane stress. Fig.4 shows stress gapwise distribution at five typical instants. They are: at the beginning of filling stage; at the end of filling stage; at the end of packing stage; when the pressure of the central position drops to zero; just before ejection. During filling, the melt material is forced into the mold. When the melt contacts the cold mold surface, a very thin layer solidifies quickly at the mold surface, in which the stress is induced as a result of material cooling. Below the surface, the stress distribution has a sharp decline. As shown in Fig.4, the stress remains uniform over a central region in which the material is essentially in a rubbery state with low elastic modulus and equals the negative of the packing pressure. As the packing stage starts, in-plane stress continues to decrease and quickly reaches the lowest value as the quickincreasing of cavity pressure. During packing, packing pressure forces the melt material into the mold to compensate for the volumetric shrinkage that occurs during cooling. In-plane stress in the core region mainly holds constant at first, and thenslowly decays as the cavity pressure. Moreover, the stress evolution corresponds to the evolution of the cavity pressure in Fig.2. The stress in the constrained solidified layers increases as a result of temperature decreasing. At the end of packing, theshape of the distribution changes and shows that relatively high stress has been built up in the surface layer, followed by a sharp decline in the region more inward. Stress in central region still remains uniform. Then, no more packing pressure is applied to the part and the cavity pressure drops quickly, which causes the compressive stress begins to decrease throughout the product. Just before ejection, the residual stress distribution consists of three distinct regions made up of two skins and a core. The stress exhibits a high surface tensile value and changes to a compressive peak value close to the surface, with the core region experiencing a parabolic peak. Fig.3 In-plate stress gapwise distribution evolution Fig.4 In-plane stress distribution in the thickness direction at some typical instants3.3 In-plane Residual Stress Distribution in FlowpathIn the injection molding, the pressure history and temperature history at different locations are not the same, which causes the variation of the in-plane stress distribution. Fig.5 shows the predicted final in-plane stress gap wise distribution along the flow path after ejection. The shape of the Stress gapwise distribution along the flowpath after ejection stress gapwise distribution is almost the same along the flowpath. However, the central tensile stress near the gate is a little lower than the stress at the locations away from the gate.4 Experimental VerificationMeasurements of residual stress are frequently carried out with the layer removal method. This method is relatively easy to apply to flat specimens and gives information about the stress distribution in the gap wise direction. Zoetelief5 successfully applied this method to polymers and investigated experimentally for specimens of amorphous polymer ABS. As shown in Fig.6, the calculated stressprofiles are compared with the experimental values in x direction and y direction. The experimental stress results are obtained from the Zoeteliefs paper. In the calculation, material and process conditions are the same to the Zoeteliefs experiment. There is a qualitative agreement between the measured and the calculated results. Moreover, to the amorphous polymer, the calculated stress in the in-plane direction is the same, since no anisotropy is taken into account.Fig.6 Calculated and measured gapwise stress distribution5 ConclusionIn the present study, we simulated theevolution and distribution of the cavity pressure and residual stress along the flowpath. Calculations with a viscoelastic mode are compared with experimental results obtained with the layer removal method for ABS specimens. Calculations show in-plane stress distribution in the thickness direction varies greatly in the injection molding process. At the beginning, there is considerable higher stress in the skin region, while the stress drops quickly below the surface and remains uniform over a central region. Just before ejection, the stress exhibits a high tensile value in surface and changes to a compressive peak value close to the surface, with the core region experiencing a parabolic tensile peak. During the filling and packing process, the shape of the gap wise stress distribution is the almost the same along the flow path. At the beginning, there is a significant variation of the stress value along flow path and then the stress tends to be uniform. After ejection, the central tensile stress near the gate is a little lower than the stress at locations away from the gate.References1 Bushko W C, Stokes V K. Solidification of thermoviscoelastic melts. Part I: formulation of model problemJ. Polymer Engineering and Science,1995, 35(4): 351-364.2 Bushko W C, Stokes V K. Solidification of thermoviscoelastic melts. Part : effects of processing conditions on shrinkage and residualstressesJ. Polymer Engineering and Science, 1995,5(4):365-383.3 Jansen K M B, Titomanlio G. Effect of pressure history on shrinkage and residual stresses-injection molding with constrained shrinkageJ. Polymer Engineering and Science, 1996, 36(15):20292040.4 Jansen K M B, Vandijk D J, Husselman M H. Effect of processing conditions on shrinkage in injection moldingJ. Polymer Engineering and Science, 1998,38(5):838-846.5 Zoetelief W F, Douven L F A. Residual thermal stresses in injection molded productsJ. Polymer Engineering and Science, 1996, 36(14):1886-1896.6 Ferry J D. Viscoelastic properties of polymersM.3rd ed. New York: John Wiley & Sons, 1980.7 Zhou H M, Li D Q. Residual stress analysis of the post-filling stage in injection mouldingJ. International Journal of Advanced Manufacturing Technology, 2005, 25(7-8): 700-704.喷射造型中残余应力的数值模拟XI Guo-dong, ZHOU Hua-min, LI De-qun (State Key Laboratory of Mold &Die Technology, Huazhong University of Science and Technology, Wuhan 430074, China)摘要: 残余应力的历史和分配是基于线形弹性模型在几何学领域被模拟出来的，以便在喷射造型过程去探究残余应力的力学发展。结果表明，残余应力的分配在沿着流程的厚度上几乎是相同的，并且评估的压力在末尾附近是高于入口附近的压力的。CLC 编号 : TQ 320.66；O 345 文件密码: 一文章身份证:1003-4951(2006)01-0017-07关键词: 注入成型; 剩余的压迫力; 数字的模拟; 弹性1 介绍喷射造型对于聚合体产品的制造是一种柔性的生产技术。 一个典型的喷射造型过程有四个阶段: 充填, 包装, 冷却和产品喷出。在这些过程，由于高压力和冷却产生残余应力，它将导致产品的扭曲和收缩。为了制造高精密的产品，制造过程中必须模拟压力和热量导致的残余应力。喷射造型的残余应力近来已经越来越被注意。一些研究者已经用不同的模型计算出过程中应力和收缩量。大体上,残余应力的研究通过独立的模型被集中在理论的分析上。它不考虑造型中的细节和与包装和冷却的联系。 在研究过程中, 几何学残余应力的分配和历史根据线形热弹模型被模拟出来。在受压力影响的部分，研究热的来源和压力的减少。数值模型是根据有限元的方法建立起来的，密度的离散分层和指定的条件有限的不同方法及时期间用分层堆积的离散化沿着厚度和在指定的边界情况之下。 被发展的模拟制度用来计算被形成部份的典型注入的剩余压迫力。2 样板的问题2.1 线性弹性模型温度和压应力来自于不同类的冷却在与以流体静力学压力的组合。对于冷却，空闲时间增加并且变成可与填充和包装时间相比较。因此，热压力的正确预测将兼具相等的黏性和弹性的构成。但是在无穷小应变变化的极限内，这兼具黏性和弹性材料的行为被很好地用线黏滞弹性的理论描述。大多数的喷射产品非常薄, 我们能采取流程方向1-空间和厚度位置方向当做那3方向而建立当地坐标。全部压力张量能被分裂为流体静力学压力和额外压力。当是增大松弛函数时，是减小松弛函数，是热力应变，球张量应变，额外疲劳张量和是物质时间。2.2 基本假定和边界情况为在喷射成型过程中进行单一化热量的计算和诱导压应力, 做出如下假定:(1) 我们采取流程方向作为1方向，厚度方向作为3方向建立当地坐标系；(2)在铸型的时候, 材料地方性地被定性在通过(主体，肋和其他的壁) 三个空间特征非平面方向, 因此，非平面处应变假设为0；(3) 正常的压力在产品的厚度方向是常数而且等于洞压力相反值;(4)只要洞压力是非零, 材料就粘在模型壁上；(5) 疏忽模型的弹力和不考虑模型的工作层的扭曲。3 结果和讨论：为了要研究压力的发展和分配，如图1所示，在样品(300 2.5 毫米 75 )的模拟能充分表现出来。着重于物理进程被提议成为最小的复杂方法,这将会在成型期间发生较好的转变。所用的材料是ABS，物质的叁数和处理叁数被列在表1和表2中。Fig.1 Rectangular strip mold3.1 洞压力的发展：依照基本的假定(3)，在模拟中，正应力与包装压力相反。因此，洞压力的发展表示了正应力的变化。图2表示了沿着流程在不同的位置的计算压力历史，包括在喷射口附近的压力分配形状。四分之一在喷射口附近，一半在尾端，附近，另四分之一在尾端和流程的尾端。在充填期间，压力的增加去克服逐渐增加的流动压力。在充填阶段结束的时候，最大的压力(63.42MPa)在喷射口附近，而最小的压力(15.62MPa)在流程的结束的附近。在这二个位置之间的一种明显的不同。当包装阶段开始的时, 洞压力在所有位置将增加而且很快地接近设定的包装压力60Mpa。而且，压力分配趋于统一。在包装阶段，材料被迫进入空穴去补偿发生在冷却期间的收缩。洞压力起初主要保持不变，当冷却达到中心区域时洞压力减小缓慢。在尾端附近补偿收缩是很困难的，在这里，压力下降迅速。洞压力在流程中趋于不一致的状况。在包装结束时，在喷射口附近的压力达到50.99MPa, 而流程结束时压力恰恰是36.75Mpa。然后,全部的洞压力将以相同的速度下降当冷却继续时。当下降到零时，部份压力在模子厚度方向上被分离而且自由地收缩，正常的压力仍保持为零。3.2 残余应力的发展我们把流动平面压力称为“非平面压力”。对于横切等方性的材料，x-方向的压力等于 y-方向的压力。 图3和图4表明了非平面压力在厚度方向的分配和它在由图1所示的中心位置P1上的发展。图3表示了非平面压力的全部发展。图4表明五种类型的缺口压力分配，如下：在填充阶段的开始;在填充阶段的结束;在包装阶段的结束; 当中央位置的压力降到零位时;在喷射之前。在充填期间，熔化的材料被压入模子。在模子表面迅速凝固为一薄层，在此压力被表现为材料冷却的结果。在表层之下，压力的分配明显下降。如图4所示, 当材料的本质是低弹性模数的橡胶状态时压力在中央的区域之上保持统一，并且和包装压力相反。当包装阶段开始时,非平面压力继续减小并快速达到最低值就像迅速增长的动压力一样。在包装期间，包装压力将熔化材料压入模子以补偿在冷却时发生的体积收缩量。非平面压力在中心区域最初保持恒定，然后像洞压力那样逐渐减少。而且，在图2中，压力的变化与洞压力相符合。在凝固层的压力随着温度的降低而增加。在包装结束的时候,分配形状的改变并且表示出在表层存在有相对的高压力，并且伴随着在更向里的方向压力迅速降低的情况。在中心区域的压力依旧保持统一不变。然后,包装压力不在适用于部分压力和洞压力迅速降低的情况。这将引起整个产品压力开始降低。在喷射之前，残余应力的分配由三种明显区域组成，该区域由两表面一核心区域组成。随着核心区域表现出峰值，应力表现为一种高表面延伸值和转变为接近于表面的有压缩性的峰值。3.3 流程中平面残余应力的分配在喷射造型中，压力历史和温度历史在不同位置是不相同的,他们引起各种形式的平面压力的分配。 图5表明了在喷射后沿着流程的最终预测平面压力的分配。缺口处压力的形式在流程中也总是相同的。然而，在入口处中心延伸压力是低于远离入口处位置的压力的。4 实验的确认残余应力的测量经常用层移的方法